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  1. Aug 24, 2007 #1
    please help me how to
    Establish the ff. properties of δ(y).

    (a) δ(y) = δ(-y)
    (b) δ(y) = δ'(y)
    (c) yδ(y)= 0
    (d) δ(ay)= 1/a δ(y)
    (e) δ(y²-a²) = [1/(2a)] [δ(y-a)+δ(y+a)]
    (g) δ(y) δ(y-a) = f(a) δ(y-a)
    (h) yδ'(y) = -δ(y)

  2. jcsd
  3. Aug 24, 2007 #2


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    You need to show some work for this sort of question and should, in future, post in the homework and coursework questions forum.

    What are you denoting by delta? Do you have a definition to work from?
  4. Aug 24, 2007 #3
    I may be wrong, but according to a) and b) the only possibility is [tex]\delta (y) = 0[/tex]. (Which is consistent with c-h).
  5. Aug 24, 2007 #4

    George Jones

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    No, [itex]\delta[/itex] is the Dirac delta "function" (distribution, actually), and this thread is in the wrong forum. It should be in either Advanced Physics or Calculus & Beyond, depending on the course for which deah received this as an assigned question.

    deah, how would you start a demsonstration of any of these properties?
  6. Aug 24, 2007 #5
    I was not aware that [tex]\delta (y) = \delta '(y)[/tex]
  7. Aug 24, 2007 #6

    George Jones

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    There must be a typo in (b); note also the typo in (g).
  8. Aug 24, 2007 #7
    First you have to choose a sequence of functions to work with whose limit is the dirac delta. For instance the sequence

    y(x,n) = n^2 x + n for -1/n < x < 0
    -n^2 x + n for 0 < x < 1/n
    0 otherwise

    Then delta(x) = lim(y(x,n),n->infinity)

    Use this sequence to prove the properties.
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